（1）证明：∵AD∥BC,∴∠DEC=∠EDA,∠BEA=∠EAD,又∵EA=ED,∴∠EAD=∠EDA,∴∠DEC=∠AEB,又∵EB=EC,∴△DEC≌△AEB,∴AB=CD,∴梯形ABCD是等腰梯形． （2）当AB⊥AC时,四边形AECD是菱形． 证明：∵AD∥BC,BE=EC=AD,∴四边形ABED和四边形AECD均为平行四边形． ∴AB=ED,∵AB⊥AC,∴AE=BE=EC,∴四边形AECD是菱形． 过A作AG⊥BE于点G,∵AE=BE=AB=2,∴△ABE是等边三角形,∴∠AEB=60°,∴AG= 3 ,∴S 菱形AECD =ECAG=2× 3 =2 3